Jose Mourinho's side prevailed 3-0 against the same opponents both at home and away in the 2013-14 competition and went into Wednesday's Group G clash in great heart after four straight Premier League wins.
In contrast, Schalke had made their worst start to a Bundesliga campaign for 46 years, picking up just one point from their first three fixtures.
However, with Diego Costa, scorer of seven of their 15 domestic goals so far this term, warming the bench, Chelsea failed to kick on and Klaas-Jan Huntelaar levelled just after an hour.
Costa was introduced for the final 20 minutes, but not even his presence could help the hosts break down Schalke's stubborn resistance for a second time.
Schalke brought back key players such as Julian Draxler and Huntelaar from Saturday's 4-1 Bundesliga loss at Borussia Monchengladbach, but captain Benedikt Howedes was one of seven players to miss out through injury.
Ramires fluffed an early chance as his shot trickled into the hands of Ralf Fahrmann, but Fabregas made no mistake when set up by Hazard after 10 minutes, although the Spaniard was fortunate not to be pulled up for a foul on Max Meyer in the build-up.
The home team continued to enjoy plenty of possession, Hazard was a constant threat whenever on the ball and Drogba got a header on target from a superb Luis cross.
Fabregas missed a glorious opportunity to double the lead on 35 minutes when blasting over the bar after Branislav Ivanovic had cut the ball back into his path from the byline.
Kevin-Prince Boateng did manage to test Thibaut Courtois with a sweetly-struck long-range strike and Draxler dragged a shot just wide after a strong run into the box prior to half-time.
And Drogba then screwed another clear-cut chance just wide before Huntelaar showed him how it should be done when cutting in from the left and firing low past Courtois on 62 minutes.
